Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Find\int \frac{6}{(x-1)(x+1)}dx 

  • Option 1)

    3ln(x+1)(x-1) +C

  • Option 2)

    3ln(x+1)/(x-1) +C

  • Option 3)

    3ln(x-1)/(x+1) +C

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we have learned

Rule of integration by Partial fraction -

Linear and non-repeated:

\frac{P(x)}{Q(x)}=\frac{P(x)}{(x-\alpha _{1})(x-\alpha _{2})\cdot \cdot \cdot (x-\alpha _{n})}

Let  \frac{P(x)}{Q(x)}=\frac{A}{(x-\alpha _{1})}+\frac{B}{(x-\alpha _{2})}\cdot \cdot \cdot

Find A,B...

By comparing N^{x} and  P(x) 

-

 

I= \int \frac{6dx}{(x-1)(x+1)}=\int \left ( \frac{A}{(x-1)}+\frac{B}{(x+1)} \right )dx

Thus 6= A(x+1)+B(x-1)  

On calculating A=3 , B= -3

Thus I= 3ln (x-1) -3ln (x+1)+ C

 

 

 

 


Option 1)

3ln(x+1)(x-1) +C

This is incorrect

Option 2)

3ln(x+1)/(x-1) +C

This is incorrect

Option 3)

3ln(x-1)/(x+1) +C

This is correct

Option 4)

none of these

This is incorrect

Posted by

Plabita

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question